Estimation of Aquifer Porosity from seismic anisotropy using Hudson Crack Model

Abstract The characterization of fracture-controlled groundwater flow systems requires quantitative methods that bridge geophysical observations with hydrogeological properties. This study presents a systematic framework integrating the Hudson crack model with seismic ambient noise tomography to transform seismic anisotropy measurements into subsurface fracture parameters relevant to a groundwater aquifer. The theoretical approach utilizes Hudson’s effective medium approximation for water-filled penny-shaped cracks to establish quantitative relationships between observed azimuthal anisotropy patterns and crack density distributions. By implementing Christoffel equation solutions for horizontally transversely isotropic media, we derive analytical expressions that relate SV-wave velocity variations to crack orientation and density, specifically leveraging the characteristic 2θ azimuthal dependence inherent to aligned fracture systems. The application to the Cape Modern aquifer system in Utah demonstrates the method’s capability to resolve groundwater aquifer characteristics from high-resolution ambient noise tomography. Analysis of continuous seismic recordings from 257 nodal stations reveals depth-dependent seismic structure and anisotropy patterns with strengths. Implementation of the Hudson crack model with water-filled penny-shaped fractures yields quantitative porosity constraints of 7-9% for the shallow aquifer at 0.09 km depth and 5-7% for the deeper one at 0.17 km. This workflow provides a quantitative framework to extract fracture porosity information from seismic anisotropy observations, complementing traditional hydrogeological methods with continuous spatial coverage at substantially lower cost than extensive drilling programs.